Modeling of Electric Machinery and Converters

Over the past two decades, Purdue researchers have been highly active in pushing the envelope in electric machinery modeling, particularly in regard to modeling machine-converter interaction. Areas of interest have included synchronous machines, induction machines, permanent magnet synchronous machines, and switched reluctance machines. Perhaps one of the most fundamental early contributions was set forth by P.C. Krause who organized reference frame theory and made its application systematic through the introduction of the arbitrary reference frame [1].

In the area of synchronous machines, Purdue has been active in extending the standard qd model to include saturation, leakage saturation, and distributed rotor effects in a systematic way [2-3], as well as finding effective means to experimentally identify parameters of this advanced model [4]. Related to this work is an model of synchronous machine models that incorporate hysteresis and multiple rectifier modes [5-6]. Together [2-6] form the basis of probably the most accurate ODE based synchronous machine model in existence.

Purdue researchers have also been highly interested in the problem of synchronous machine – line commutated converter interaction. In [7], Purdue researchers were the first to identify the true value of commutating reactance of a synchronous machine, which is critical to modeling of generator-rectifier sets. This methodology was extended in [8-10] to form a comprehensive analysis of this class of systems.

Purdue researchers have also been very active in the modeling of induction machines. The works set forth in [11-12] put forth a model which includes saturation, leakage saturation, and distributed rotor effects in a comprehensive fashion. These effects are critical if the performance in the understanding of the current and torque ripple (and related acoustic noise) in induction motor based drive systems. A means of experimentally identifying parameters is set forth in [13]. Purdue researchers have also created advanced induction machine models using magnetic equivalent circuit (MEC) analysis in order to help understand the implications of issues such as broken rotor bars [14].

Single-phase induction machines (actually two-phase machines suitably connected to a single-phase source) are particularly difficult to model. The performance of ‘single’ phase machines has also been considered by Purdue researchers in [15-16].

Purdue has had a long standing interest in permanent magnet synchronous machine drives. The range from older studies considering the operating modes possible with 120o voltage source converters [17-19] to more recent studies which considering wide-bandwidth machine models designed to accurately predict current ripple levels [20] or in which the machine back emf has an arbitrary waveshapes [21].

The area of switched reluctance machine modeling is particularly challenging because of the high degree of magnetic saturation and highly non-sinusoidal inductance variation. Despite this Purdue researchers have developed relatively straightforward models [22-23] and even models in which state variables are constant in the steady state [24]. Purdue researchers have even modeled rather exotic variations of this device, including a switched capacitive machine [25].